$6.$ Consider the following information:

State of Economy Probability of State of Economy Rate of Return if State Occurs

Stock A Stock B Stock C

Boom $\mathrm{.}66\mathrm{.}09\mathrm{.}03\mathrm{.}24$

Bust $\mathrm{.}34\mathrm{.}13\mathrm{.}19\mathrm{.}04$

a$.$ What is the expected return on an equally weighted portfolio of these three stocks?

b$.$ What is the variance of a portfolio invested $21$ percent each in A and B and $58$ percent in C$?$